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Sladkaya [172]
2 years ago
12

27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 47 college students are randomly sele

cted, find the probability that
a. Exactly 13 of them major in STEM.
b. At most 12 of them major in STEM.
c. At least 9 of them major in STEM.
d. Between 8 and 15 (including 8 and 15) of them major in STEM.
Mathematics
1 answer:
scoray [572]2 years ago
5 0

Answer:

0.12995

0.47508

0.0841

0.738

Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

Zscore = −1.378

P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04

-1.378 ≤ z ≤ 0.924

Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

P(Z ≤ - 1.378) = 0.084102

0.82226 - 0.084102

= 0.738

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